Partitioning net ecosystem carbon exchange into net assimilation and ...

GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 18, GB2019, doi:10.1029/2003GB002166, 2004

Partitioning net ecosystem carbon exchange into net assimilation and respiration with canopy-scale isotopic measurements: An error propagation analysis with 13CO2 and CO18O data J. Ogeé,1,2 P. Peylin,3 M. Cuntz,1,4 T. Bariac,3 Y. Brunet,5 P. Berbigier,5 P. Richard,3 and P. Ciais1 Received 2 October 2003; revised 24 March 2004; accepted 9 April 2004; published 18 June 2004.

[1] Stable CO2 isotope measurements are increasingly used to partition the net CO2

exchange between terrestrial ecosystems and the atmosphere in terms of nonfoliar respiration (FR) and net photosynthesis (FA) in order to better understand the variations of this exchange. However, the accuracy of the partitioning strongly depends on the isotopic disequilibrium between these two gross fluxes, and a rigorous estimation of the errors on FA and FR is needed. In this study, we account for and propagate uncertainties on all terms in the mass balance and isotopic mass balance equations for CO2 in order to get accurate estimates of the errors on FA and FR. We apply our method to a maritime pine forest in the southwest of France. Nighttime Keeling plots are used to estimate the 13 C and 18O isotopic signature of FR (dR), and for both isotopes the a priori uncertainty associated with this term is estimated to be around 2% at our site. Using d13C-CO2 and [CO2] measurements, we then show that the uncertainty on instantaneous values of FA and FR can be as large as 4 mmol m2 s1. Even if we could get more accurate estimates of the net CO2 flux, the isoflux, and the isotopic signatures of FA and FR, this uncertainty would not be significantly reduced because the isotopic disequilibrium between FA and FR is too small, around 2–3%. With d18O-CO2 and [CO2] measurements the uncertainty associated with the gross fluxes lies also around 4 mmol m2 s1 but could be dramatically reduced if we were able to get more accurate estimates of the CO18O isoflux and the associated discrimination during photosynthesis. This is because the isotopic disequilibrium between FA and FR is large, of the order of 12–17%. The isotopic disequilibrium between FA and FR and the uncertainty on dR vary among ecosystems and over the year. Our approach should help to choose the best strategy to study the INDEX TERMS: 4806 carbon budget of a given ecosystem using stable isotopes. Oceanography: Biological and Chemical: Carbon cycling; 0315 Atmospheric Composition and Structure: Biosphere/atmosphere interactions; 1615 Global Change: Biogeochemical processes (4805); KEYWORDS: carbon cycle, carbon 13, oxygen 18, CO2 assimilation, respiration Citation: Ogeé, J., P. Peylin, M. Cuntz, T. Bariac, Y. Brunet, P. Berbigier, P. Richard, and P. Ciais (2004), Partitioning net ecosystem carbon exchange into net assimilation and respiration with canopy-scale isotopic measurements: An error propagation analysis with 13 CO2 and CO18O data, Global Biogeochem. Cycles, 18, GB2019, doi:10.1029/2003GB002166.

1. Introduction 1

Laboratoire des Sciences du Climat et de l’Environnement, Commissariat a´ l’Energie Atomique-Saclay, Gif-sur-Yvette, France. 2 Now at Ecologie Fonctionnelle et Physique de l’Environnement, Institut National de la Recherche Agronomique-Bordeaux, Villenave d’Ornon, France. 3 Laboratoire de Biogeóchimie des Milieux Continentaux, Centre National de la Recherche Scientifique, Institut National de la Recherche Agronomique, Universite´ de Pierre et Marie Curie, Paris, France. 4 Now at Research School of Biological Sciences, Australian National University, Canberra, Australia. 5 Ecologie Fonctionnelle et Physique de l’Environnement, Institut National de la Recherche Agronomique-Bordeaux, Villenave d’Ornon, France. Copyright 2004 by the American Geophysical Union. 0886-6236/04/2003GB002166$12.00

[2] Terrestrial ecosystems are a major component of the global carbon cycle, mainly through the exchange of CO2 with the atmosphere. The spatial and temporal variations of this exchange are difficult to assess because they involve several physical and biological processes acting at different scales. In the absence of any disturbance the net CO2 exchange (F) between terrestrial ecosystems and the atmosphere is the result of carbon uptake during daytime by photosynthesis (gross primary production (GPP)) and carbon losses by respiration (total ecosystem respiration (TER)). TER is a composite flux, comprising respiration by foliage, stem, and roots (autotrophic respiration) and respiration by soil organisms (heterotrophic respiration).

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OGEÉ ET AL.: PARTITIONING NET CO2 FLUX WITH ISOTOPES

On a process basis it is more appropriate to decompose F into net assimilation FA (jFAj = jGPPj – foliar respiration) and nonfoliar respiration FR (FR = TER – foliar respiration) because gross photosynthesis and daytime foliar respiration are likely to share a common energy pool [e.g., Dewar et al., 1999] and are indistinguishable through measurements. [3] The net CO2 flux is now measured continuously at more than 100 continental sites within the worldwide FluxNet network using the eddy covariance technique [Aubinet et al., 2000; Baldocchi et al., 2001]. Combined with air CO2 storage measurements, this leads to accurate and continuous estimates of F at a half-hourly timescale and over several years (up to 10 years at some sites). However, partitioning F into its component fluxes FA and FR is necessary if we want to understand the spatial and seasonal or interannual variations of the net exchange [Janssens et al., 2001; Valentini et al., 2000]. This implies the use of multitechnique approaches [Canadell et al., 2000; Running et al., 1999]. [4] Stable CO2 isotope measurements, combined with CO2 eddy flux and concentration measurements, can potentially be used to do the partitioning [Yakir and Wang, 1996; Bowling et al., 2001]. Indeed, FR and FA have different CO2 isotope signatures so that the total CO2 mass balance and the isotopic (13CO2 or CO18O) mass balance equations are not proportional. Using the notations recommended by Bowling et al. [2003a], we will write FA þ FR ¼ F

ð1aÞ

dA F A þ dR F R ¼ F d :

ð1bÞ

Equations (1a) and (1b) are the mass balance and the isotopic mass balance equations for CO2, respectively. The isotopic signature of FA is dA = da – Dcanopy (further decomposed into the isotopic ratio of atmospheric CO2, da, and the whole canopy integrated isotope discrimination during photosynthesis, Dcanopy), dR is the daytime isotopic signature of FR, and Fd is called isoflux. In the case of CO18O the mass balance equation can be more complex because the isotopic composition of daytime respiration is expected to be nonuniform [e.g., Langendo¨rfer et al., 2002] and to involve the so-called ‘‘invasion’’ flux, i.e., the diffusion of ambient CO2 into the soil, followed by partial isotopic equilibration with soil water and retrodiffusion [Miller et al., 1999; Tans, 1998]. We will assume that equation (1b) holds for CO18O, and we will try to account indirectly for these complications. Provided that the isotopic signatures of FR and FA, the flux F, and the isoflux Fd are known, equation (1) can be used to retrieve FA and FR. [5] At present, it is not possible to get direct measurements of Fd. Only indirect methods exist based on flask air sample measurements of d13C-CO2 and [CO2] [Bowling et al., 2003a]. In addition, nighttime isotopic mixing lines referred to as ‘‘Keeling plots’’ are commonly used to quantify dR [Pataki et al., 2003]. [6] Bowling et al. [2001] used a ‘‘big-leaf’’ modeling approach to estimate Dcanopy for 13CO2 and to partition F

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into FA and FR at a temperate deciduous forest over a mean daily cycle. They showed that the partitioning was sensitive to the degree of isotopic disequilibrium between FA and FR and to the bulk stomatal conductance model used to compute Dcanopy. Ogeé et al. [2003b] further tested this partitioning method at a temperate coniferous forest. Using a multilayer multileaf model [Ogeé et al., 2003a], they tested each assumption made by Bowling et al. for the determination of the bulk isotopic signatures dR and Dcanopy and the isoflux in the 13CO2 mass balance equation. They found that neglecting the mesophyll resistance for CO2 diffusion could lead to inaccurate estimates of FA and FR. Also, taking advantage of a stronger isotopic disequilibrium in midafternoon between FA and FR [Baldocchi and Bowling, 2003; Ogeé et al., 2003b], they showed that only a subset of isotopic measurements is necessary to partition F into FA and FR over a 3-week mean daily cycle. Langendo¨rfer et al. [2002] used the CO18O mass balance equation (in conjunction with the total CO2 mass balance equation) to estimate cumulative FA and FR and showed that the partitioning was quite sensitive to the parameterization used to compute Dcanopy and especially to the mesophyll resistance to CO2 diffusion. [7] In all these studies the authors performed sensitivity analyses of the partitioning to some parameters used to estimate Dcanopy. The model used to compute Dcanopy and the values of dR, da, F, or Fd were taken as granted, although we know there are nonnegligible errors associated with them. For instance, Baldocchi and Bowling [2003] estimate that the relative sampling error on the instantaneous value of da can reach 35% when flasks are collected only once every 30 min. A first objective of this paper is to propagate uncertainties on all terms in equation (1) when partitioning F into FA and FR with isotopic measurements. For this, we use the same d13C-CO2 and [CO2] data set as Ogeé et al. [2003b] but propose a different resolution of the system based on a probabilistic approach. Not only will the parameters (FA and FR in our case) be estimated but also their standard errors, given prior values and uncertainties for dR, dA, F, and Fd. [8] Differences in the isotopic signatures of FA and FR are crucial for an accurate partitioning. At a half-hourly timescale the isotopic disequilibrium is expected to be mainly driven by the diurnal variations in photosynthetic discrimination. For d13C-CO2 data this disequilibrium may be small, especially in established ecosystems where the d13C values of decomposing and newly fixed carbon are very similar. In contrast, for d18O-CO2 data it is expected to be strong because CO2 equilibrates isotopically with leaf or soil water and the d18O values of leaf water have much larger diurnal variations than those of soil water [Yakir and Sternberg, 2000]. This may provide a significant advantage for CO 18 O over 13 CO 2 as a tracer for partitioning net ecosystem exchange into photosynthesis and respiration. This advantage, however, may be restricted by the larger scatter and the difficulty in measuring the isoflux Fd from d18O-CO2 data [Bowling et al., 1999]. A second objective of this paper is to apply our partitioning (with error propagation) using either d13C-CO2 or d18O-CO2 data (or both) in order to evaluate which

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tracer has the best potential to separate FA and FR in the carbon budget.

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4 September 1997. The accuracy of the isotopic measurements is ±0.3% for d13C-CO2 and ±0.5% for d18O-CO2, but sampling error (air flasks are filled after 1 min only) may significantly increase these numbers.

2. Material and Methods 2.1. Research Area [9] The experimental site is located 20 km from Bordeaux, France (44420N, 0460W, altitude 62 m), in a nearly homogeneous maritime pine stand (Pinus pinaster) planted in 1970. The trees are distributed in parallel rows along a NE-SW axis with an interrow distance of 4 m. In September 1997, when the isotopic measurements were performed, the stand density was 520 trees per hectare. The mean tree height was 18 m, and the projected leaf area index was around 3. The canopy stays confined in the top 6 m [Porte´ et al., 2000] so that canopy and understory are two separate layers. The latter mainly consists of grass (Molinia coerulea) whose roots and clumps remain throughout the year but whose leaves are green only from April to late November, with maximum leaf area index and height of 1.4 – 2.0 m and 0.6 – 0.8 m, respectively [Loustau and Cochard, 1991]. A 5-cm-thick litter layer made of compacted grass and dead needles is present all year long. In September 1997 the soil water content in the top 80 cm went down to 60 mm so that the effect of water stress on CO2 and water vapor exchange was noticeable. 2.2. Flux and Meteorological Measurements [10] The flux and meteorological measurements were performed following the requirements of EUROFLUX [Aubinet et al., 2000]. At 25 m above ground, considered here as our reference level, the following data were measured and averaged over 30 min: net radiation, incident solar radiation, air temperature and specific humidity, rainfall (at 20 m), wind speed, friction velocity, sensible and latent heat fluxes, and CO2 fluxes. Details are given by Berbigier et al. [2001]. [11] Air CO2 concentration measurements were performed at 11 heights (0.01, 0.2, 0.7, 1, 2, 6, 10, 14, 18, 25, and 38 m) during a 2-month period starting on 4 September 1997. Each level was sampled for 2 min, and the retrieval of a 30-min time series at each level was done by linear interpolation. The overall precision of the [CO2] measurements was estimated as ±10 ppm, which includes both measurement and sampling errors. Details are given by Ogeé et al. [2003b]. 2.3. Isotope Measurements [12] All isotopic measurements were performed during a single 22-hour period from 4 September 1997 at 0500 UT to 5 September 1997 at 0300 UT with a high resolution in space and time. Ambient air samples from the same 11 levels used for [CO2] were collected every half hour (night) or every hour (day) into glass flasks for isotopic analysis. A total of 341 flasks were analyzed. Details are given by Ogeé et al. [2003b]. [13] Tree sap and foliage (needle and leaf) samples were also collected for stable isotope analysis every hour from trees and grass near the mast. Soil profiles were drilled from 0 to 0.5 m below the surface at 0930 and 1330 UT on

2.4. Flux Partitioning and Error Propagation [14] Equation (1) can be seen as a linear system with two equations to two unknowns. So far, this system has been solved ‘‘exactly’’ at each time step [Bowling et al., 2001; Langendo¨rfer et al., 2002; Ogeé et al., 2003b], assuming no correlation from one time step to the next. In order to deal with data uncertainty and data redundancy in a natural manner, we use here a probabilistic approach, widely used in geophysical problems and based on a general inverse Bayesian formalism [Tarantola, 1987]. In this formalism the objective can be reformulated as follows: Given a priori information on the gross fluxes FA and FR and some uncertainties in the physical model that relates FA and FR to F and Fd (equation (1)), how should one modify this a priori information to account for some uncertain observations? [15] Practically, the resolution of this inverse problem is done by minimizing a cost function J that accounts for both the distance (deviation) between the ‘‘modeled’’ net fluxes (H(x), the left-hand side of equation (1)) and their measured counterparts (y0, the right-hand side of equation (1)), and the distance between a priori values of FA and FR (xb = {FAb; FbR}) and their optimized a posteriori values (x = {FA; FR}), all distances being weighted with some a priori uncertainties (standard deviations s): 2 !2 1 4 FA þ FR F 2 dA FA þ dR FR Fd 2 FA FAb J¼ þ þ 2 sF sFd sbFA !2 3 FR FRb 5 ð2aÞ þ sbFR

or in a matrix form J¼

1 t 1 ½HðxÞ yo t C1 o ½HðxÞ yo þ ðx xb Þ Cb ðx xb Þ ; 2 ð2bÞ

where superscripts 1 and t indicate the inverse and the transpose matrices and Co and Cb are variance/covariance matrices that contain on their diagonals the uncertainties on the observations and the a priori gross fluxes, respectively. The second term on the right-hand side of equation (2) is a regularization term (so-called Bayesian term) that allows a solution to be defined even with fewer equations than unknowns or with linearly dependent equations. [16] Equation (2b) is, in fact, more general and leads to equation (2a) only if we suppose that FA and FR or F and Fd are independent variables, so that Co and Cb are diagonal matrices. In this paper, we will make this assumption. Also, we will assume that the fluxes from one time step to the next are not correlated so that equation (1) can be inverted at each time step independently of the mass balances at other time steps. This is not completely true because we know, for

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example, that the respiration flux varies smoothly during daytime. We feel that it is reasonable to ignore this complication for the present study, although it should be addressed in future work. [17] As a first step, we thus need to define uncertainties on the observations ({sF; sFd}) together with prior values (xb = {FAb; FbR}) and prior uncertainties ({sbFA; sbFR}) for the parameters (gross fluxes). A classical assumption is to suppose the parameters and the observations to be normally distributed. In the case of a linear problem such as equation (1) the solution, i.e., the optimized values (xa) and uncertainties (Ca) for the parameters, is then given by xa ¼ xb þ Ca H0t C1 o ½yo Hðxb Þ

ð3aÞ

0 1 1 Ca ¼ H0t C1 ; o H þ Cb

ð3bÞ

with H0

@H 1 1 ¼ : dA dR @x

ð3cÞ

The major advantage of this approach, compared to the ‘‘exact’’ inversion of equation (1), relies on the estimation of the posterior uncertainties (diagonal terms of Ca) from known data errors Co. These posterior uncertainties directly quantify the stability of the solution xa. Indeed, the more independent the equations are (in a linear sense), the smaller the uncertainties Ca will be. Note that these posterior uncertainties are independent of the value of the observations y0. This property will be used in section 3.6 to assess the potential of the d18O-CO2 data in terms of error reduction on the gross fluxes FA and FR, even without any reliable measurements of the corresponding isoflux Fd. Finally, note that if we do not account for a priori information, then the diagonal terms of Cb are infinite, and those of Ca are given by equation (3b), which reduces to s2FA ¼

s2FR ¼

dR dR dA

dA dR dA

2

2

s2F þ

s2F þ

1 dR dA

1 dR dA

2

2

s2Fd

ð4aÞ

s2Fd :

ð4bÞ

Equation (4) can also be obtained more simply by solving equation (1) and then formally propagating the uncertainties. However, our approach (equation (3b)) is more general, with the advantage that it can deal with a system with more or fewer equations than unknowns. This is the case when we want to retrieve FA and FR with the three mass balance equations derived for total CO2, 13CO2, and CO18O. [18] As will be seen in section 3.2, the isotopic signatures dA and dR are also largely uncertain and should be considered, together with FA and FR, as unknown parameters with prior values (xb) and prior uncertainties (Cb) that need to be optimized. Such a formulation slightly complicates the

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minimization of J, H(x) becoming nonlinear with respect to x, and equation (3a) has to be solved iteratively according to [Tarantola, 1987, p. 196]. n 0 n n xnþ1 ¼ xb þ Cna H0t xna C1 a o yo H xa H xa xb xa : ð5Þ

Both approaches (with and without solving for the isotopic signatures) are compared in section 3.4. 2.5. Multilayer Multileaf MuSICA Model [19] For the present study we also used the multilayer multileaf MuSICA model [Ogeé et al., 2003a], in which we incorporated the transport of d18O-CO2 and d18O-H2O (Appendix A). The transport of d13C-CO2 had already been incorporated in the model [Ogeé et al., 2003b]. MuSICA gives independent estimates of the discrimination Dcanopy, the isoflux Fd, and the gross fluxes FA and FR in a coherent framework. Its ability to reproduce the d18O-H2O of leaf water and the vertical gradients of [CO2], d13C-CO2, and d18O-CO2 at different times of the day has been evaluated, but we refer the reader to Appendix A for further details [see also Ogeé et al., 2003b] because it is not the major focus of this study. In this paper, the model is used only as an independent estimator to test and validate our ability to assess the discriminations and the gross fluxes with simpler models such as equation (1).

3. Results and Discussion 3.1. Meteorological Conditions [20] Meteorological variables and CO2 isotopic compositions above the vegetation (at the reference height of 25 m) are shown in Figure 1 on the day when isotopic measurements were made. No rain occurred during the experiment, and in daytime the sky was clear most of the time. Air temperature and relative humidity were anticorrelated with a maximum temperature occurring at 1530 UT. Wind speed was relatively low during the whole day. Low wind speed is usually accompanied by strong air storage terms, especially during the night and the beginning of the day. This is true in our case where [CO2] builds up during the night and until 1000 UT, while d13C-CO2 decreases. In contrast, d18O-CO2 keeps a relatively constant value (around 0.5% Vienna Peedee belemnite (VPDB)-CO2) during the whole period. The importance of total CO2 and 13CO2 air storage in the mass balance equations and its role in the recycling of respired CO2 have already been observed and described by Lloyd et al. [1996]. 3.2. Value and Uncertainty for DR [21] To solve equation (1a), the value of the daytime nonfoliar respired CO2 signature (dR) is needed. We set this value to the intercept of the regression of da versus 1/Ca during nighttime, where Ca is the air CO2 mole fraction. Such a regression, commonly called a ‘‘Keeling plot’’ [Keeling, 1958], is supposed to be a two-pool mixing line between a ‘‘background’’ CO2 and a respired CO2 source, and its intercept (dR,n) is then the isotopic signature of the respiration source (subscript n indicates that it is a nighttime

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shown in Figure 2. For d13C-CO2 data the value of dR,n is dR,n(13C) = 26.8 ± 0.1% VPDB, i.e., exactly as given by Ogeé et al. [2003b], while for d18O-CO2 data we have dR,n(18O) = 7.9 ± 0.2% VPDB-CO2. [23] According to Miller and Tans [2003] these relatively small errors on dR,n indicate that the whole nighttime data set is well described by a two-pool mixing line. Qualitatively, this means that nighttime CO2 sources are nearly steady over the night. However, by making a Keeling plot regression at each time step with the same d13C-CO2 data set, Ogeé et al. [2003b] found no clear temporal variation in dR,n(13C) but found a scatter between all time steps (0.3%) 3 times as large as the error on the intercept shown in Figure 2. On other ecosystems, Still et al. [2003], Bowling et al. [2003b], and Lai et al. [2003] also found significant variations in dR,n(13C) throughout the night. For d18O-CO2 data the steadiness of the source is even more questionable. Indeed, respired CO2 exchanges 18O atoms with the surrounding water while it diffuses away from the sources so that foliar respiration equilibrates with bulk leaf water while soil respiration equilibrates with soil water, and bulk leaf water enrichment at night is expected to decrease more rapidly than soil water. For example, in our study, the isotopic composition of soil water changes by